Sizes of Solar System Objects

Introduction

Often in astronomy, the term “think big” is under-thought by the general public. Most people don’t realize the HUGE distances and sizes involved in understanding something even as small as the solar system. This is epitomized by science fiction writers who almost always under-estimate the distances between objects.

For example, I was just watching an episode of Star Trek Voyager when someone mentioned that an object was relatively close, about 3 million km away. It was some anomaly in space. Now, this is a show where the ship is stranded on the other side of the galaxy, and they typically are traveling at speeds far in excess of light. 3 million km away is 2% the distance between Earth and the sun, and it takes light only 10 seconds to travel that distance. In other words, this object would be there and gone well before anyone could reasonably react, relay the information, make a command decision, and then have that decision implemented … the writers dramatically under-estimated the distances here.

I wanted to directly address this with a post comparing the sizes of objects in the solar system: Sun, Jupiter, Earth, and Moon.

Length, Area, and Volume

Forgive me if this seems like a trivial section, but often people do not realize how these three things are related and how they scale:

Length is the distance between two points. It is 1-dimensional.

Area is a region covered by an object in 2 dimensions. The area of an object is related to length². It has units of length².

Volume is how much 3-dimensional “area” an object covers. The volume of an object is related to length³. It has units of length³.

Ratios

Rather than get into exact numbers in this post, I thought I’d spare you all some math and use nice, round numbers in a ratio form. In this exercise, Sun = 1:

Length/Radius/Diameter:

• Sun: 1
• Jupiter: 0.1
• Earth: 0.01
• Moon: 0.0025

In other words, it would only take 10 Jupiters to fit across the sun. This is probably considerably less than you thought – length-wise, the sun really isn’t too much larger than Jupiter … or even Earth, where 100 Earths would fit across the sun.

Area:

• Sun: 1
• Jupiter: 0.01
• Earth: 0.0001
• Moon: 0.000006

Now we’re getting to something that probably makes more intuitive sense with what you may have been taught. Area-wise, there seems to be a much larger difference between these solar system objects. It would take 100 Jupiters tiled across the sun to block it out. This actually has direct application to discovering extra-solar planets:

With the transit method of finding exoplanets, a planet passes in front of its host star as seen from Earth. This dims the light from the star (since the exoplanet blocks it) and hence we can measure this dimming. If a Jupiter-like planet passes in front of a sun-like star, then it dims the light by 1%. This actually allows us to directly measure the diameter of the transiting planet AND hence calculate its density.

Volume:

• Sun: 1
• Jupiter: 0.0001
• Earth: 0.0000001
• Moon: 0.00000002

This is probably more like what you learned in school: The sun is “so big” that it would take 1 million Earths to fill it up. Which is true – it would take 100^3 (length-cubed) Earths to do this. Volume is also a measure of material – the sun has over 99.9% of the material in the solar system. And this is often quoted (actually I think the number that’s more often quoted is “over 99.98%”). This is why people think the sun is so large compared with what we think of in our every-day lives.

The Point

My point in going through this is that there was a post in a skeptics forum today by someone claiming that he came across the “myth” that the moon is “only” 400x smaller than the sun (or the sun “only” 400x larger than the moon). He thought that this was false, when in fact it wasn’t.

A probable reason as to why he thought it was false is that we generally think of volume when we think of the sizes of solar system objects, and, volumetrically, the moon is vastly smaller than the sun. But, length-wise, the moon really is only 400x smaller than the sun.

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